Solution - Linear equations with two unknowns

System of Linear Equations entered :

  [1]           4x-2y=14
  [2]           y=1/2x-1

Equations Simplified or Rearranged :

   [1]    4x - 2y = 14
   [2]    -x/2 + y = -1

// To remove fractions, multiply equations by their respective LCD

     Multiply equation [2] by 2


// Equations now take the shape:

   [1]    4x - 2y = 14
   [2]    -x + 2y = -2

Graphic Representation of the Equations :

    -2y + 4x = 14        2y - x = -2  

  
 

Solve by Substitution :

// Solve equation [2] for the variable  x 
 

  [2]    x = 2y + 2

// Plug this in for variable  x  in equation [1]

   [1]    4•(2y+2) - 2y = 14
   [1]    6y = 6

// Solve equation [1] for the variable  y 

   [1]    6y = 6 

   [1]    y = 1 

// By now we know this much :

    x = 2y+2
    y = 1

// Use the  y  value to solve for  x 

    x = 2(1)+2 = 4 

Solution :

 {x,y} = {4,1}